Abstract
This study examined the participation of a group of middle school students in an after-school mathematics club as they worked on cryptography problems. The analysis focused on interactions characterized by collective problem-solving activity, when intellectual work was distributed and various students took on active problem-solving roles, paying particular attention to intersections between task structures and positioning moves. We found that all open-ended tasks—those tasks that afforded multiple strategies and had multiple solutions—resulted in at least some collective problem solving, though it was not always sustained (Turner, Gutierrez, & Sutton, 2009). We also found that the task structures, in combination with interactive positioning moves by facilitators and students, served to sustain or disrupt collective problem-solving activity.
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